A variational derivation is used to obtain a series of higher order theories along with the associated boundary conditions for thick layers of transversely isotropic materials with symmetric modes of deformation. Through use of the MACSYMA symbolic manipulation program, several higher, i.e., sixth-, eighth-, and twelfth-order theories for transversely isotropic materials have been obtained. In order to establish the present layer theories, the displacements are taken as polynomials in powers of z with two-dimensional coefficient functions. These polynomials are truncated from polynomials expanded from the exact displacements in three-dimensional elasticity in order to get approximate solutions of the exact theory. Therefore, the displacement functions in the present sixth-, eighth-, and twelfth-order thick layer theories are assumed in the form of even terms in z for u and v and odd for w. The stress resultants are given and expressed in terms of displacement functions and are applied to derive the determinant of the homogeneous version of the equilibrium equations.

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